/**
 * data-structure-typed
 * @author Kirk Qi
 * @copyright Copyright (c) 2022 Kirk Qi <qilinaus@gmail.com>
 * @license MIT License
 */
import type { Comparator, DFSOrderPattern, ElementCallback, HeapOptions } from '../../types';
import { IterableElementBase } from '../base';
/**
 * 1. Complete Binary Tree: Heaps are typically complete binary trees, meaning every level is fully filled except possibly for the last level, which has nodes as far left as possible.
 * 2. Heap Properties: Each node in a heap follows a specific order property, which varies depending on the type of heap:
 * Max Heap: The value of each parent node is greater than or equal to the value of its children.
 * Min Heap: The value of each parent node is less than or equal to the value of its children.
 * 3. Root Node Access: In a heap, the largest element (in a max heap) or the smallest element (in a min heap) is always at the root of the tree.
 * 4. Efficient Insertion and Deletion: Due to its structure, a heap allows for insertion and deletion operations in logarithmic time (O(log n)).
 * 5. Managing Dynamic Data Sets: Heaps effectively manage dynamic data sets, especially when frequent access to the largest or smallest elements is required.
 * 6. Non-linear Search: While a heap allows rapid access to its largest or smallest element, it is less efficient for other operations, such as searching for a specific element, as it is not designed for these tasks.
 * 7. Efficient Sorting Algorithms: For example, heap sort. Heap sort uses the properties of a heap to sort elements.
 * 8. Graph Algorithms: Such as Dijkstra's shortest path algorithm and Prime's minimum-spanning tree algorithm, which use heaps to improve performance.
 * @example
 * // Use Heap to sort an array
 *     function heapSort(arr: number[]): number[] {
 *       const heap = new Heap<number>(arr, { comparator: (a, b) => a - b });
 *       const sorted: number[] = [];
 *       while (!heap.isEmpty()) {
 *         sorted.push(heap.poll()!); // Poll minimum element
 *       }
 *       return sorted;
 *     }
 *
 *     const array = [5, 3, 8, 4, 1, 2];
 *     console.log(heapSort(array)); // [1, 2, 3, 4, 5, 8]
 * @example
 * // Use Heap to solve top k problems
 *     function topKElements(arr: number[], k: number): number[] {
 *       const heap = new Heap<number>([], { comparator: (a, b) => b - a }); // Max heap
 *       arr.forEach(num => {
 *         heap.add(num);
 *         if (heap.size > k) heap.poll(); // Keep the heap size at K
 *       });
 *       return heap.toArray();
 *     }
 *
 *     const numbers = [10, 30, 20, 5, 15, 25];
 *     console.log(topKElements(numbers, 3)); // [15, 10, 5]
 * @example
 * // Use Heap to merge sorted sequences
 *     function mergeSortedSequences(sequences: number[][]): number[] {
 *       const heap = new Heap<{ value: number; seqIndex: number; itemIndex: number }>([], {
 *         comparator: (a, b) => a.value - b.value // Min heap
 *       });
 *
 *       // Initialize heap
 *       sequences.forEach((seq, seqIndex) => {
 *         if (seq.length) {
 *           heap.add({ value: seq[0], seqIndex, itemIndex: 0 });
 *         }
 *       });
 *
 *       const merged: number[] = [];
 *       while (!heap.isEmpty()) {
 *         const { value, seqIndex, itemIndex } = heap.poll()!;
 *         merged.push(value);
 *
 *         if (itemIndex + 1 < sequences[seqIndex].length) {
 *           heap.add({
 *             value: sequences[seqIndex][itemIndex + 1],
 *             seqIndex,
 *             itemIndex: itemIndex + 1
 *           });
 *         }
 *       }
 *
 *       return merged;
 *     }
 *
 *     const sequences = [
 *       [1, 4, 7],
 *       [2, 5, 8],
 *       [3, 6, 9]
 *     ];
 *     console.log(mergeSortedSequences(sequences)); // [1, 2, 3, 4, 5, 6, 7, 8, 9]
 * @example
 * // Use Heap to dynamically maintain the median
 *     class MedianFinder {
 *       private low: MaxHeap<number>; // Max heap, stores the smaller half
 *       private high: MinHeap<number>; // Min heap, stores the larger half
 *
 *       constructor() {
 *         this.low = new MaxHeap<number>([]);
 *         this.high = new MinHeap<number>([]);
 *       }
 *
 *       addNum(num: number): void {
 *         if (this.low.isEmpty() || num <= this.low.peek()!) this.low.add(num);
 *         else this.high.add(num);
 *
 *         // Balance heaps
 *         if (this.low.size > this.high.size + 1) this.high.add(this.low.poll()!);
 *         else if (this.high.size > this.low.size) this.low.add(this.high.poll()!);
 *       }
 *
 *       findMedian(): number {
 *         if (this.low.size === this.high.size) return (this.low.peek()! + this.high.peek()!) / 2;
 *         return this.low.peek()!;
 *       }
 *     }
 *
 *     const medianFinder = new MedianFinder();
 *     medianFinder.addNum(10);
 *     console.log(medianFinder.findMedian()); // 10
 *     medianFinder.addNum(20);
 *     console.log(medianFinder.findMedian()); // 15
 *     medianFinder.addNum(30);
 *     console.log(medianFinder.findMedian()); // 20
 *     medianFinder.addNum(40);
 *     console.log(medianFinder.findMedian()); // 25
 *     medianFinder.addNum(50);
 *     console.log(medianFinder.findMedian()); // 30
 * @example
 * // Use Heap for load balancing
 *     function loadBalance(requests: number[], servers: number): number[] {
 *       const serverHeap = new Heap<{ id: number; load: number }>([], { comparator: (a, b) => a.load - b.load }); // min heap
 *       const serverLoads = new Array(servers).fill(0);
 *
 *       for (let i = 0; i < servers; i++) {
 *         serverHeap.add({ id: i, load: 0 });
 *       }
 *
 *       requests.forEach(req => {
 *         const server = serverHeap.poll()!;
 *         serverLoads[server.id] += req;
 *         server.load += req;
 *         serverHeap.add(server); // The server after updating the load is re-entered into the heap
 *       });
 *
 *       return serverLoads;
 *     }
 *
 *     const requests = [5, 2, 8, 3, 7];
 *     console.log(loadBalance(requests, 3)); // [12, 8, 5]
 * @example
 * // Use Heap to schedule tasks
 *     type Task = [string, number];
 *
 *     function scheduleTasks(tasks: Task[], machines: number): Map<number, Task[]> {
 *       const machineHeap = new Heap<{ id: number; load: number }>([], { comparator: (a, b) => a.load - b.load }); // Min heap
 *       const allocation = new Map<number, Task[]>();
 *
 *       // Initialize the load on each machine
 *       for (let i = 0; i < machines; i++) {
 *         machineHeap.add({ id: i, load: 0 });
 *         allocation.set(i, []);
 *       }
 *
 *       // Assign tasks
 *       tasks.forEach(([task, load]) => {
 *         const machine = machineHeap.poll()!;
 *         allocation.get(machine.id)!.push([task, load]);
 *         machine.load += load;
 *         machineHeap.add(machine); // The machine after updating the load is re-entered into the heap
 *       });
 *
 *       return allocation;
 *     }
 *
 *     const tasks: Task[] = [
 *       ['Task1', 3],
 *       ['Task2', 1],
 *       ['Task3', 2],
 *       ['Task4', 5],
 *       ['Task5', 4]
 *     ];
 *     const expectedMap = new Map<number, Task[]>();
 *     expectedMap.set(0, [
 *       ['Task1', 3],
 *       ['Task4', 5]
 *     ]);
 *     expectedMap.set(1, [
 *       ['Task2', 1],
 *       ['Task3', 2],
 *       ['Task5', 4]
 *     ]);
 *     console.log(scheduleTasks(tasks, 2)); // expectedMap
 */
export declare class Heap<E = any, R = any> extends IterableElementBase<E, R> {
    /**
     * The constructor initializes a heap data structure with optional elements and options.
     * @param elements - The `elements` parameter is an iterable object that contains the initial
     * elements to be added to the heap.
     * It is an optional parameter, and if not provided, the heap will
     * be initialized as empty.
     * @param [options] - The `options` parameter is an optional object that can contain additional
     * configuration options for the heap.
     * In this case, it is used to specify a custom comparator
     * function for comparing elements in the heap.
     * The comparator function is used to determine the
     * order of elements in the heap.
     */
    constructor(elements?: Iterable<E> | Iterable<R>, options?: HeapOptions<E, R>);
    protected _elements: E[];
    /**
     * The function returns an array of elements.
     * @returns The element array is being returned.
     */
    get elements(): E[];
    /**
     * Get the size (number of elements) of the heap.
     */
    get size(): number;
    /**
     * Get the last element in the heap, which is not necessarily a leaf node.
     * @returns The last element or undefined if the heap is empty.
     */
    get leaf(): E | undefined;
    /**
     * Static method that creates a binary heap from an array of elements and a comparison function.
     * @returns A new Heap instance.
     * @param elements
     * @param options
     */
    static heapify<E = any, R = any>(elements: Iterable<E>, options: HeapOptions<E, R>): Heap<E>;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * The add function pushes an element into an array and then triggers a bubble-up operation.
     * @param {E} element - The `element` parameter represents the element that you want to add to the
     * data structure.
     * @returns The `add` method is returning a boolean value, which is the result of calling the
     * `_bubbleUp` method with the index `this.elements.length - 1` as an argument.
     */
    add(element: E): boolean;
    /**
     * Time Complexity: O(k log n)
     * Space Complexity: O(1)
     *
     * The `addMany` function iterates over elements and adds them to a collection, returning an array of
     * boolean values indicating success or failure.
     * @param {Iterable<E> | Iterable<R>} elements - The `elements` parameter in the `addMany` method is
     * an iterable containing elements of type `E` or `R`. The method iterates over each element in the
     * iterable and adds them to the data structure. If a transformation function `_toElementFn` is
     * provided, it transforms the element
     * @returns The `addMany` method returns an array of boolean values indicating whether each element
     * in the input iterable was successfully added to the data structure.
     */
    addMany(elements: Iterable<E> | Iterable<R>): boolean[];
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @returns The top element or undefined if the heap is empty.
     */
    poll(): E | undefined;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Peek at the top element of the heap without removing it.
     * @returns The top element or undefined if the heap is empty.
     */
    peek(): E | undefined;
    /**
     * Check if the heap is empty.
     * @returns True if the heap is empty, otherwise false.
     */
    isEmpty(): boolean;
    /**
     * Reset the elements of the heap. Make the elements empty.
     */
    clear(): void;
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * Clear and add elements of the heap
     * @param elements
     */
    refill(elements: E[]): boolean[];
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(1)
     *
     * Use a comparison function to check whether a binary heap contains a specific element.
     * @param element - the element to check.
     * @returns Returns true if the specified element is contained; otherwise, returns false.
     */
    has(element: E): boolean;
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(1)
     *
     * The `delete` function removes an element from an array-like data structure, maintaining the order
     * and structure of the remaining elements.
     * @param {E} element - The `element` parameter represents the element that you want to delete from
     * the array `this.elements`.
     * @returns The `delete` function is returning a boolean value. It returns `true` if the element was
     * successfully deleted from the array, and `false` if the element was not found in the array.
     */
    delete(element: E): boolean;
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(log n)
     *
     * Depth-first search (DFS) method, different traversal orders can be selected。
     * @param order - Traverse order parameter: 'IN' (in-order), 'PRE' (pre-order) or 'POST' (post-order).
     * @returns An array containing elements traversed in the specified order.
     */
    dfs(order?: DFSOrderPattern): E[];
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * Clone the heap, creating a new heap with the same elements.
     * @returns A new Heap instance containing the same elements.
     */
    clone(): Heap<E, R>;
    /**
     * Time Complexity: O(n log n)
     * Space Complexity: O(n)
     *
     * Sort the elements in the heap and return them as an array.
     * @returns An array containing the elements sorted in ascending order.
     */
    sort(): E[];
    /**
     * Time Complexity: O(n log n)
     * Space Complexity: O(n)
     *
     * Fix the entire heap to maintain heap properties.
     */
    fix(): boolean[];
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * The `filter` function creates a new Heap object containing elements that pass a given callback
     * function.
     * @param callback - The `callback` parameter is a function that will be called for each element in
     * the heap. It takes three arguments: the current element, the index of the current element, and the
     * heap itself. The callback function should return a boolean value indicating whether the current
     * element should be included in the filtered list
     * @param {any} [thisArg] - The `thisArg` parameter is an optional argument that specifies the value
     * to be used as `this` when executing the `callback` function. If `thisArg` is provided, it will be
     * passed as the `this` value to the `callback` function. If `thisArg` is
     * @returns The `filter` method is returning a new `Heap` object that contains the elements that pass
     * the filter condition specified by the `callback` function.
     */
    filter(callback: ElementCallback<E, R, boolean>, thisArg?: any): Heap<E, R>;
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * The `map` function creates a new heap by applying a callback function to each element of the
     * original heap.
     * @param callback - The `callback` parameter is a function that will be called for each element in
     * the heap. It takes three arguments: `el` (the current element), `index` (the index of the current
     * element), and `this` (the heap itself). The callback function should return a value of
     * @param comparator - The `comparator` parameter is a function that defines the order of the
     * elements in the heap. It takes two elements `a` and `b` as arguments and returns a negative number
     * if `a` should be placed before `b`, a positive number if `a` should be placed after
     * @param [toElementFn] - The `toElementFn` parameter is an optional function that converts the raw
     * element `RR` to the desired type `T`. It takes a single argument `rawElement` of type `RR` and
     * returns a value of type `T`. This function is used to transform the elements of the original
     * @param {any} [thisArg] - The `thisArg` parameter is an optional argument that allows you to
     * specify the value of `this` within the callback function. It is used to set the context or scope
     * in which the callback function will be executed. If `thisArg` is provided, it will be used as the
     * value of
     * @returns a new instance of the `Heap` class with the mapped elements.
     */
    map<EM, RM>(callback: ElementCallback<E, R, EM>, comparator: Comparator<EM>, toElementFn?: (rawElement: RM) => EM, thisArg?: any): Heap<EM, RM>;
    protected _DEFAULT_COMPARATOR: (a: E, b: E) => number;
    protected _comparator: Comparator<E>;
    /**
     * The function returns the value of the _comparator property.
     * @returns The `_comparator` property is being returned.
     */
    get comparator(): Comparator<E>;
    /**
     * The function `_getIterator` returns an iterable iterator for the elements in the class.
     */
    protected _getIterator(): IterableIterator<E>;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Float operation to maintain heap properties after adding an element.
     * @param index - The index of the newly added element.
     */
    protected _bubbleUp(index: number): boolean;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Sinking operation to maintain heap properties after removing the top element.
     * @param index - The index from which to start sinking.
     * @param halfLength
     */
    protected _sinkDown(index: number, halfLength: number): boolean;
}
export declare class FibonacciHeapNode<E> {
    element: E;
    degree: number;
    left?: FibonacciHeapNode<E>;
    right?: FibonacciHeapNode<E>;
    child?: FibonacciHeapNode<E>;
    parent?: FibonacciHeapNode<E>;
    marked: boolean;
    /**
     * The constructor function initializes an object with an element and a degree, and sets the marked
     * property to false.
     * @param {E} element - The "element" parameter represents the value or data that will be stored in
     * the node of a data structure. It can be any type of data, such as a number, string, object, or
     * even another data structure.
     * @param [degree=0] - The degree parameter represents the degree of the element in a data structure
     * called a Fibonacci heap. The degree of a node is the number of children it has. By default, the
     * degree is set to 0 when a new node is created.
     */
    constructor(element: E, degree?: number);
}
export declare class FibonacciHeap<E> {
    /**
     * The constructor function initializes a FibonacciHeap object with an optional comparator function.
     * @param [comparator] - The `comparator` parameter is an optional argument that represents a
     * function used to compare elements in the FibonacciHeap. If a comparator function is provided, it
     * will be used to determine the order of elements in the heap. If no comparator function is
     * provided, a default comparator function will be used.
     */
    constructor(comparator?: Comparator<E>);
    protected _root?: FibonacciHeapNode<E>;
    /**
     * The function returns the root node of a Fibonacci heap.
     * @returns The method is returning either a FibonacciHeapNode object or undefined.
     */
    get root(): FibonacciHeapNode<E> | undefined;
    protected _size: number;
    /**
     * The function returns the size of an object.
     * @returns The size of the object, which is a number.
     */
    get size(): number;
    protected _min?: FibonacciHeapNode<E>;
    /**
     * The function returns the minimum node in a Fibonacci heap.
     * @returns The method is returning the minimum node of the Fibonacci heap, which is of type
     * `FibonacciHeapNode<E>`. If there is no minimum node, it will return `undefined`.
     */
    get min(): FibonacciHeapNode<E> | undefined;
    protected _comparator: Comparator<E>;
    /**
     * The function returns the comparator used for comparing elements.
     * @returns The `_comparator` property of the object.
     */
    get comparator(): Comparator<E>;
    /**
     * Get the size (number of elements) of the heap.
     * @returns {number} The size of the heap.  Returns 0 if the heap is empty. Returns -1 if the heap is invalid.
     */
    clear(): void;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Insert an element into the heap and maintain the heap properties.
     * @param element
     * @returns {FibonacciHeap<E>} FibonacciHeap<E> - The heap itself.
     */
    add(element: E): FibonacciHeap<E>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Insert an element into the heap and maintain the heap properties.
     * @param element
     * @returns {FibonacciHeap<E>} FibonacciHeap<E> - The heap itself.
     */
    push(element: E): FibonacciHeap<E>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Peek at the top element of the heap without removing it.
     * @returns The top element or undefined if the heap is empty.
     * @protected
     */
    peek(): E | undefined;
    /**
     * Time Complexity: O(n), where n is the number of elements in the linked list.
     * Space Complexity: O(1)
     *
     * Get the size (number of elements) of the heap.
     * @param {FibonacciHeapNode<E>} head - The head of the linked list.
     * @protected
     * @returns FibonacciHeapNode<E>[] - An array containing the elements of the linked list.
     */
    consumeLinkedList(head?: FibonacciHeapNode<E>): FibonacciHeapNode<E>[];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * @param parent
     * @param node
     */
    mergeWithChild(parent: FibonacciHeapNode<E>, node: FibonacciHeapNode<E>): void;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @returns The top element or undefined if the heap is empty.
     */
    poll(): E | undefined;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @returns The top element or undefined if the heap is empty.
     */
    pop(): E | undefined;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * merge two heaps. The heap that is merged will be cleared. The heap that is merged into will remain.
     * @param heapToMerge
     */
    merge(heapToMerge: FibonacciHeap<E>): void;
    /**
     * Create a new node.
     * @param element
     * @protected
     */
    createNode(element: E): FibonacciHeapNode<E>;
    /**
     * Default comparator function used by the heap.
     * @param {E} a
     * @param {E} b
     * @protected
     */
    protected _defaultComparator(a: E, b: E): number;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Merge the given node with the root list.
     * @param node - The node to be merged.
     */
    protected mergeWithRoot(node: FibonacciHeapNode<E>): void;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @param node - The node to be removed.
     * @protected
     */
    protected removeFromRoot(node: FibonacciHeapNode<E>): void;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @param y
     * @param x
     * @protected
     */
    protected _link(y: FibonacciHeapNode<E>, x: FibonacciHeapNode<E>): void;
    /**
     * Time Complexity: O(n log n)
     * Space Complexity: O(n)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @protected
     */
    protected _consolidate(): void;
}